A particle of mass \(m\) is attached to one end of a light inextensible string of length \(a\). The other end of the string is attached to a fixed point \(O\). The point \(A\) is such that \(O A=a\) and \(O A\) makes an angle \(\alpha\) with the upward vertical, where \(\tan \alpha=\frac{12}{5}\). The particle is projected downwards from \(A\) with speed \(u\) perpendicular to the string and moves in a vertical plane (see diagram). The string becomes slack after the string has rotated through \(270^{\circ}\) from its initial position, with the particle now at the point \(B\).
(i) Show that \(u^{2}=2 a g\).

(ii) Find the maximum tension in the string as the particle moves from \(A\) to \(B\).